Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD plus QED

Results computed in lattice QCD + QED are presented for the electromagnetic mass splittings of the low-lying hadrons. These are used to determine the renormalized, nondegenerate, light quark masses. It is found that m(u) ((MS) over bar) = 2.24(10)(34), m(d)((MS) over bar) = 4.65(15)(32), and m(s)((MS) over bar) = 97.6(2.9)(5.5) MeV at the renormalization scale 2 GeV, where the first error is statistical and the second systematic. We find the lowest-order electromagnetic splitting (m(pi+) - m(pi 0))(QED) = 3.38(23) MeV, the splittings including next-to-leading order, (m(pi+) - m(pi 0))(QED) = 4.50(23) MeV, (m(K+) - m(K0))(QED) = 1.87(10) MeV, and the m(u) not equal m(d) contribution to the kaon mass difference, (m(K+) - m(K0))((mu - md)) = 5.840(96) MeV. All errors are statistical only, and the next-to-leading-order pion splitting is only approximate in that it does not contain all next-to-leading-order contributions. We also computed the proton-neutron mass difference, including for the first time, QED interactions in a realistic 2 + 1 flavor calculation. We find (m(p) - m(n))(QED) = 0.383(68) MeV, m(p) - m(n))((mu - md)) = -2.51(14) MeV (statistical errors only), and the total m(p) - m(n) = -2.13(16) x (70) MeV, where the first error is statistical, and the second, part of the systematic error. The calculations are carried out on QCD ensembles generated by the RBC and UKQCD collaborations, using domain wall fermions and the Iwasaki gauge action (gauge coupling beta = 2.13 and lattice cutoff a(-1) approximate to 1.78 GeV). We use two lattice sizes, 16(3) and 24(3) ((1.8 fm)(3) and (2.7 fm)(3)), to address finite-volume effects. Noncompact QED is treated in the quenched approximation. The valence pseudoscalar meson masses in our study cover a range of about 250 to 700 MeV, though we use only those up to about 400 MeV to quote final results. We present new results for the electromagnetic low-energy constants in SU(3) and SU(2) partially quenched chiral perturbation theory to the next-to-leading order, obtained from fits to our data. Detailed analysis of systematic errors in our results and methods for improving them are discussed. Finally, new analytic results for SU(2)(L) x SU(2)(R)-plus-kaon chiral perturbation theory, including the one-loop logs proportional to alpha(em)m, are given.